Yes, aloe vera goes bad. Generally speaking, aloe vera gel is good for 10 days in the fridge. You may be able to extend the shelf life of aloe vera gel a little by mixing in some vitamin E, lavender, or tea tree oil.
The leaves should give you a clue, but you can also check the saucer under the container. If it's moist or there's standing water, you're probably overwatering. If it's bone...
Get some fresh, healthy leaves. Wash them thoroughly and let them dry. Check the bottom (broader) side of the leaves to see if there is any yellow discharge. If there...
There shouldn't be a problem if you're using the natural plant gel without added chemicals. Over-the-counter aloe vera usually isn't pure and can cause allergies or further inflammation.
Aloe vera is a natural antiseptic and it has anti-inflammatory and healing properties. It will accelerate the healing process for your skin, reduce pain, swelling, and help with blood clotting.
